When power coupling devices are used to inductively transfer electric power in noncontact fashion, e.g., from stationary subsystems to rotating subsystems in medical CT scanners or the like, it is often desired that such power coupling devices be shielded. Lack of adequate shielding may, for example, result in undesirable RF emission, increased leakage inductance, and/or reduced power transfer efficiency. Moreover, where power is being transferred between or among bodies capable of engaging in relative rotation, it may be impossible or impractical to employ an unbroken Faraday cage or other such integral shield that would completely surround the power coupling device, it being instead necessary to employ a shield that only partially encloses the power coupling device or to divide such shield into multiple parts split so as to form gap(s) permitting relative rotation between or among such bodies.